I think we have to find a fold here. We have to be good here a good percentage of the time, and a river overbet shove is almost always the nuts. I seriously doubt he would overbet shove with a weaker two pair. People overbet because they want to get maximum value. A lot of times, I overbet shove the river with the nuts to make it look like a bluff, like I want a fold. I've gotten hero called by KK with a four to a straight on a board and an A when I overbet 4x the pot on the river with my rivered set of threes in a 3-bet pot. Gotten called by underpairs, TPGK, second pair to the board, etc. Oh, and overbetting with the nut straight with four to a straight has made me tons of money. People can never a fold straight, and one time I got some guy to hero me with two pair when I overbet 20x the pot (lol). I actually folded a straight in one hand; it was so sick. After I got raised on the turn and bombed all-in overbet on the river, there wasn't a single hand I could put him on other than j10o on a Q8795 board when I held 56s.
We are beating none of his value range, which are basically sets and at the very bottom of it AJ. And the A hits our range very hard, so it's less likely he's bluffing at it. We've shown a lot of strength by check-calling oop twice and leading the river, but yet he still jams over us.
Also, what I find a lot of people do is when they flop a nutted hand, they bet small to keep you in. And then they bomb the river in a last effort to get maximum value. On the flop and turn he basically bet half-pot. I think if he really wanted you to fold and was semi-bluffing with Q10 or something, he'd bet 60-66% on flop and/or turn to get you off your hand. The bet sizing throughout this hand looks like he was just luring you in and bombed the river in a last attempt to get huge value when he realized you rivered a strong hand. I just think that against an unknown, most of the time we are not good here. People tend to be very unbalanced in their play, and a river overbet shove is heavily skewed towards nutted hands. I mean, the way you played the hand, it could look like you were stubborn with AK because the bets were so small. That's a terrible way to play AK unless you had some sick reads, but I wouldn't be surprised if some players would check-call AK OOP twice readless. Unless it is Bovada Zone, I seriously doubt many would even try getting someone off TPTK, overpair, or better.